It's a program similar to AOL's Instant Messenger (AIM) that let's you see when your friends are online and instantly send msgs/chat back and forth. I use both ICQ and AIM. For more info, check out the ICQ homepage.
I've used ICQ way longer than AIM, and don't really have a clear-cut favorite. ICQ has more features, but AIM is faster and easier to use (most of my friends who don't know much about computers use it). It's a matter of personal preference I guess. I use both.